Existence of solutions for a class of the boundary value problem of fractional \(q\)-difference inclusions
type: Item
instance of: scholarly article
title: Existence of solutions for a class of the boundary value problem of fractional \(q\)-difference inclusions
zbMATH Open document ID: 1379.39008
author: Nana Jin
author: Shurong Sun
author: Guanwei Chen
published in: Journal of Applied Mathematics and Computing
publication date: 2017-11-10T00:00:00Z
review text: This paper studies the existence of solutions for a class of boundary value problems (BVP) of fractional \(q\)-difference inclusions \[ \left(^cD_q^\alpha x\right)(t)\in F\left (t, ^cD_q^\sigma x(t)\right), \;\;0\leq t\leq 1, \] subject to the boundary conditions \[ x(0)=g(x),\;\;D_q^2 x(0)=0,\;\;\gamma \left(D_q x\right)(1)=\beta D_q^2 x(1), \] with \(2<\alpha\leq 3\), \(0<q<1\), \(0<\sigma<1\), \(\beta\gamma\geq 0\), \(g\) is a continuous function, and \(F:[0,1]\times \mathbb{R}\rightarrow \mathcal{P}(\mathbb{R})\) is a multivalued map. The first section is devoted to literature reviews. In the second section, the authors provide some introductions and a few basic properties and lemmas. The main result is given in the third section. The authors obtain sufficient conditions such that the main BVP has at least one solution on \([0, 1]\). Moreover, they provide an example in the last section to demonstrate the application. This paper will be of interest to anyone who is studying fractional \(q\)-difference equations.
reviewed by: Fei Xue
Mathematics Subject Classification ID: 39A13
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6805495
zbMATH Keywords: fractional \(q\)-difference inclusions
zbMATH Keywords: boundary value problems
zbMATH Keywords: existence of solutions
zbMATH Keywords: fixed point theorem
zbMATH Keywords: fractional \(q\)-difference equations
MaRDI profile type: Publication
full work available at URL: s12190-016-1043-6
OpenAlex ID: W2515667805
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DOI: 10.1007/S12190-016-1043-6
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description: scientific article; zbMATH DE number 6805495